docs(shutdown): revalidate task inventory

[josecelano]

Summary

Revalidates the production shutdown task inventory after #1586 adopted direct JoinSet supervision.

• Separates direct supervisor components, the narrow legacy periodic-job registry, component-owned children, detached controllers, and framework-owned request work.
• Records the persistent completed-statistics listener and configuration-dependent task cardinality.
• Captures direct-binary SIGTERM evidence: cooperative component shutdown, closed listeners, expected legacy-job deadline aborts, and process exit.
• Maps the remaining gaps to the existing Overhaul: Tracker Shutdown #1488 roadmap without changing runtime behavior or adding a new migration slice.
• Refactors the inventory into a concise overview table with detailed supporting records.

Closes #1588

Validation

• linter all
• git diff --check
• TORRUST_GIT_HOOKS_LOG_DIR=.tmp ./contrib/dev-tools/git/hooks/pre-commit.sh
• Pre-push checks: nightly format and workspace check, documentation build, and full test suite
• Direct tracker-binary SIGTERM scenario

[Copilot]

🟡 Changes recommended

The updated long-lived task inventory frontmatter links issue specs by file path instead of stable issue #NNNN references, which conflicts with the documented semantic-links convention.

Once you've addressed the issues Copilot identified, you can request another Copilot review.

Pull request overview

This PR updates the shutdown-process documentation to reflect the post-#1586 implementation reality, revalidating the production task ownership inventory and recording concrete SIGTERM shutdown evidence to close issue #1588.

Changes:

• Replaces the placeholder #1588 verification notes with implementation-time inventory evidence and manual SIGTERM observations.
• Updates the #1588 issue spec to reflect completed acceptance criteria and to point at the verification record instead of planning-time assertions.
• Refactors the shutdown task inventory into a verified overview table plus detailed supporting records, including configuration-dependent cardinality and remaining roadmap gaps.

File summaries

File	Description
docs/issues/open/1588-review-shutdown-process-for-all-tasks-jobs/verification.md	Adds implementation-time validation evidence, gap mapping, and SIGTERM verification notes.
docs/issues/open/1588-review-shutdown-process-for-all-tasks-jobs/ISSUE.md	Updates the issue spec timestamps and marks acceptance criteria complete with updated references.
docs/features/shutdown-process/task-inventory.md	Converts the inventory from draft/planning to verified/implementation-time with an overview table and detailed evidence.

Review details

• Files reviewed: 3/3 changed files
• Comments generated: 1
• Review effort level: Lite

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[josecelano]

ACK 39e264e